Abstract
Instabilities in Geomechanics appear on multiple scales involving multiple physical processes. They appear often as planar features of localised deformation (faults), which can be relatively stable creep or display rich dynamics, sometimes culminating in earthquakes. To study those features, we propose a fundamental physics-based approach that overcomes the current limitations of statistical rule-based methods and allows a physical understanding of the nucleation and temporal evolution of such faults. In particular, we formulate the coupling between temperature and pressure evolution in the faults through their multiphysics energetic process(es). We analyse their multiple steady states using numerical continuation methods and characterise their transient dynamics by studying the time-dependent problem near the critical Hopf points. We find that the global system can be characterised by a homoclinic bifurcation that depends on the two main dimensionless groups of the underlying physical system. The Gruntfest number determines the onset of the localisation phenomenon, while the dynamics are mainly controlled by the Lewis number, which is the ratio of energy diffusion over mass diffusion. Here, we show that the Lewis number is the critical parameter for dynamics of the system as it controls the time evolution of the system for a given energy supply (Gruntfest number).
Highlights
Understanding instabilities in the earth is important for disaster management, risk assessment and insurance
The reasons for using this approach are that the dynamics related to earthquake and fault motion are likely stochastic rather than deterministic in nature [1,2,3], making approaches that aim at physics-based forecasting of deterministic dynamics just part of the whole story
A systematic analysis of the effect of the Damköhler number on instabilities is well-documented in combustion physics, e.g., [15]
Summary
Understanding instabilities in the earth is important for disaster management, risk assessment and insurance. One angle of approach to mathematically predict the observed rich dynamics is to perform laboratory experiments and characterize their behaviour with simple geomechanical parametrization (e.g., rate and state variable friction) and apply these laboratory laws to the large field lengthand time-scales [4,5,6]. Another approach is to record the rich dynamics via geophysical methods and formulate mathematical rule-based models that reproduce their dynamics [7]. Both approaches have far failed to deliver predictive tools
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